In recent work (arXiv: 2008.01607), we characterize all infinite-dimensional graded modules for the Thompson group whose graded traces are certain weight 3/2 weakly holomorphic modular forms satisfying special properties. In this talk, I will demonstrate how we can use one such module to study the ranks of certain families of elliptic curves. In particular, this serves as an example of moonshine being used to answer questions in number theory.
The talk will start with a pre-seminar at 2pm:
Title: "What is... Moonshine?"
Abstract: Moonshine began as a series of numerical coincidences connecting finite groups to modular forms but has since evolved into a rich theory that sheds light on the underlying algebraic structures that these coincidences reflect. In this talk, I will give a brief history of moonshine, describe some of the existing examples of the phenomenon in the literature, and discuss how my work fits into the story.